What are some suitable positive functions as activations of neural networks?
First of all: an activation function is usually placed after a linear operation and you can have a lot of them (maybe different) in your nn. That's why it would be better to say $\bf a$ activation function of the neural net and not $\bf the$ activation function. So if you meant by activation function the last operation which is going to make your outputs non-negative, then you're right, ReLU isn't a good choice. Usually when people need to output some positive values, they take exponent as the last operation. I used it several times and everything was just fine.